32 DOC. 49 JULY 1907 49. To Wilhelm Wien Bern, 23 August [July] 1907[1] Highly esteemed Professor Wien:[2] You have raised here a most interesting question! Immediately after I received your letter I threw myself into this matter and have arrived at the following preliminary results. 1. I defined as the "group velocity" U the velocity with which a (slow) change of amplitude is propagated; this is, after all, the quantity at issue. I found (for arbitrarily strong absorption): U = V · - 1 J + X dV ' V dX X wavelength (in vacuum) V velocity of light (in the medium) which agrees, with an accuracy adequate for the present, with the value V - X mentioned by you. 2. In my opinion, there is a contradiction with the principle of relativity in conjunction with the principle of the constancy of the velocity of light in the vacuum if for a spec, metal and a specific color U L (velocity of light in vacuum). 3. The propagation of an electromagnetic signal with superluminal velocity is also incompatible with Maxwell's theory of electricity & light. This follows from the results of a study by Wiechert that was published in the Lorentz Festschrift.[3] In this study it is shown that one obtains something equivalent to Maxwell's equations if one introduces certain actions-at-a-distance that propagate with the velocity of light L in the vacuum and act from one electric mass to the other. Let A be a point from which an electromagn. influence can emanate, and B a point in which the influence emanating from A can be perceived. Let P, Q, R, etc. be electromagnetically active, stationary corpuscles out of which the propagation-mediating medium under investigation is imagined to be composed. Let an influence propagate from A. An action-at-a-distance is hereby generated in AB B at time unless it is compensated by processes of the following kind: L Emission in A-from here action-at-distance in P-emission in P-excitation in Q by the action-at-distance from P-etc.-excitation in B. The whole process can be conceived of as being composed of such indirect actions from A to B and of the first-mentioned direct action. From this one can easily conclude AB that at least the time must lapse before the first excitation in B, which is to say that